Michael J. Dinneen

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Nature is not only a source of minerals and precious stones but is also a mine of algorithms. By observing and studying natural phenomena, computer algorithms can be extracted. In this note, a simple natural phenomenon is used to design a sorting algorithm for positive integers, called here Bead–Sort. The algorithm’s run– time complexity ranges from O(1) to(More)
The first language we consider is the language of propositional logic. It is based on propositions (or declarative sentences) which can either be true or false. Some examples are: 1. Grass is green. 2. The sky is yellow. 3. Every natural number n > 2 is the sum of two prime numbers. 4. If I do not study then I get an F in this course. Sentence (1) is(More)
A Chaitin Omega number is the halting probability of a universal Chaitin (selfdelimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing, converging sequence of rationals) and random (its binary expansion is an algorithmic random sequence). In particular, every Omega number is strongly non-computable.(More)
The irreducible indeterminacy of individual quantum processes postulated by Born [1–3] implies that there exist physical “oracles,” which are capable of effectively producing outputs which are incomputable. Indeed, quantum indeterminism has been proved [4] under some “reasonable” side assumptions implied by Bell-, Kochen-Specker-, and(More)
Guessing the degree of difficulty of a problem before seeing its solution is notoriously hard not only for beginners, but also for the most experienced professionals. Can we develop a method to evaluate, in some objective way, the difficulty of an open problem? This note proposes such a measure which can be used for a fairly large class of finitely(More)
Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals. In this paper, we describe a general-purpose method for nding obstructions by using a bounded treewidth (or(More)